Expansion of a 100 m steel bridge deck over 50 °C

Answer: change in length = 0.06 m (change in length 60 mm, new length 100.06 m).

What we know

Original length: 100 m
Expansion coefficient α: 0.000012 1/K
Temperature change: 50 K (or °C)

α = 12 × 10⁻⁶ /K, a typical value for structural steel.

Step by step

Given: L₀ = 100 m, α = 0.000012 1/K, ΔT = 50 K (or °C)
Formula: ΔL = α × L₀ × ΔT
Substitute: ΔL = 0.000012 × 100 × 50
Result: ΔL = 0.06 m

All results

Change in length	0.06 m
Change in length	60 mm
New length	100.06 m

Open the thermal expansion calculator with these numbers → and change any of them.

The physics

Almost everything grows when it warms and shrinks when it cools, because heat makes atoms vibrate harder and sit slightly further apart. Linear thermal expansion captures this for a length: the change equals the coefficient α times the original length times the temperature change. Long objects and big temperature swings give the biggest movements.